High dynamic range display devices

ABSTRACT

A display has a screen which incorporates a light modulator. The screen may be a front projection screen or a rear-projection screen. Elements of the light modulator may be controlled to adjust the intensity of light emanating from corresponding areas on the screen. The display may provide a high dynamic range.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No. 11/351,962 filed on 10 Feb. 2006 which is a continuation of U.S. patent application Ser. No. 11/1 12,428 filed on 22 Apr. 2005 which is a divisional of U.S. patent application Ser. No. 10/469,473 (accorded filing date 27 Aug. 2003), which is the U.S. National Stage of International Application No. PCT/CA02/00255 filed on 27 Feb. 2002, which claims the benefit of U.S. Provisional Patent Application No. 60/271,563 filed on 27 Feb. 2001 and entitled HIGH DYNAMIC RANGE COLOUR DISPLAY AND PROJECTION TECHNOLOGY. These prior applications are incorporated herein by this reference.

TECHNICAL FIELD

The invention relates to displays for displaying digital images.

BACKGROUND

Dynamic range is the ratio of intensity of the highest luminance parts of a scene and the lowest luminance parts of a scene. For example, the image projected by a video projection system may have a maximum dynamic range of 300:1.

The human visual system is capable of recognizing features in scenes which have very high dynamic ranges. For example, a person can look into the shadows of an unlit garage on a brightly sunlit day and see details of objects in the shadows even though the luminance in adjacent sunlit areas may be thousands of times greater than the luminance in the shadow parts of the scene. To create a realistic rendering of such a scene can require a display having a dynamic range in excess of 1000:1. The term “high dynamic range” means dynamic ranges of 800:1 or more.

Modern digital imaging systems are capable of capturing and recording digital representations of scenes in which the dynamic range of the scene is preserved. Computer imaging systems are capable of synthesizing images having high dynamic ranges. However, current display technology is not capable of rendering images in a manner which faithfully reproduces high dynamic ranges.

Blackham et al., U.S. Pat. No. 5,978,142 discloses a system for projecting an image onto a screen. The system has first and second light modulators which both modulate light from a light source. Each of the light modulators modulates light from the source at the pixel level. Light modulated by both of the light modulators is projected onto the screen.

Gibbon et al., PCT Application No. PCT/US01/21367 discloses a projection system which includes a pre modulator. The pre modulator controls the amount of light incident on a deformable mirror display device. A separate pre-modulator may be used to darken a selected area (e.g. a quadrant).

There exists a need for cost effective displays capable of reproducing a wide range of light intensities in displayed images.

SUMMARY

This invention provides displays for displaying images and methods for displaying images. One aspect of the invention provides a display comprising: a light source; a first spatial light modulator located to modulate light from the light source; a display screen comprising a second spatial light modulator; and, an optical system configured to image light modulated by the first spatial light modulator onto a first face of the display screen.

Another aspect of the invention provides a display comprising: a light source; a first spatial light modulator located to modulate light from the light source, the first spatial light modulator comprising an array of controllable pixels; and, a second spatial light modulator located to modulate light modulated by the first spatial light modulator the second spatial light modulator comprising an array of controllable pixels; wherein each pixel of one of the first and second spatial light modulators corresponds to a plurality of pixels of the other one of the first and second light modulators.

Another aspect of the invention provides a display device comprising: first spatial modulation means for providing light spatially modulated at a first spatial resolution; second spatial modulation means for further spatially modulating the light at a second resolution different from the first resolution; and, means for controlling the first and second spatial modulation means to display an image defined by image data.

A still further aspect of the invention provides a method for displaying an image having a high dynamic range. The method comprises: generating light, spatially modulating the light according to image data in a first light modulating step; and, imaging the spatially modulated light onto a screen comprising a light modulator.

Further aspects of the invention and features of specific embodiments of the invention are described below.

BRIEF DESCRIPTION OF THE DRAWINGS

In drawings which illustrate non-limiting embodiments of the invention,

FIG. 1 is a schematic illustration of a display according to one embodiment of the invention;

FIG. 1A is a schematic illustration of a specific implementation of the display of FIG. 1;

FIG. 2 is a schematic illustration of a display according to an alternative embodiment of the invention comprising four spatial light modulators;

FIG. 3 is a schematic illustration of a rear-projection-type display according to a further embodiment of the invention;

FIG. 4 is a schematic illustration of a front-projection-type display according to a still further embodiment of the invention;

FIG. 5 is a drawing illustrating a possible relationship between pixels in a higher-resolution spatial light modulator and pixels in a lower-resolution spatial light modulator in a display according to the invention;

FIG. 5A illustrates an effect of providing one light modulator which has lower resolution than another light modulator;

FIG. 6 is a schematic illustration of a front-projection-type color display having an alternative projector construction;

FIGS. 6A and 6B are expanded cross-sectional views of portions of the front-projection screen of the color display of FIG. 6;

FIG. 7 is a graph illustrating how light imaged onto a higher-resolution light modulator from pixels of a lower-resolution light modulator can overlap to yield a smooth variation in light intensity with position; and,

FIG. 7A is a graph illustrating how the variation in light intensity with position for the image of a pixel of a light modulator can be represented as the convolution of a square profile and a spread function.

DESCRIPTION

Throughout the following description, specific details are set forth in order to provide a more thorough understanding of the invention. However, the invention may be practiced without these particulars. In other instances, well known elements have not been shown or described in detail to avoid unnecessarily obscuring the invention. Accordingly, the specification and drawings are to be regarded in an illustrative, rather than a restrictive, sense.

This invention provides displays capable of rendering images with high dynamic ranges. Displays according to the invention comprise two light modulating stages. Light passes through the stages in series to provide an image which has an increased dynamic range.

FIG. 1 illustrates schematically a display 10 according to a simple embodiment of the invention. The sizes of elements and distances between them in FIG. 1 are not to scale. Display 10 comprises a light source 12. Light source 12 may, for example, comprise a projection lamp such as an incandescent lamp or an arc lamp, a laser, or another suitable source of light. Light source 12 may comprise an optical system comprising one or more mirrors, lenses or other optical elements which cooperate to deliver light to the rest of display 10.

In the illustrated embodiment, light from light source 12 is directed toward a first light modulator 16. Light source 12 preferably provides substantially uniform illumination of first light modulator 16. Light modulator 16 comprises an array of individually addressable elements. Light modulator 16 may comprise, for example, a LCD (liquid crystal display), which is an example of a transmission-type light modulator or a DMD (deformable mirror device), which is an example of a reflection-type light modulator. Display driver circuitry (not shown in FIG. 1) controls the elements of light modulator 16 according to data which defines an image being displayed.

Light which has been modulated by first light modulator 16 is imaged onto a rear-projection screen 23 by a suitable optical system 17. Light from a small area of first light modulator 16 is directed by optical system 17 to a corresponding area on rear-projection screen 23. In the illustrated embodiment, optical system 17 comprises a lens having a focal length f. In general, the optical system 17 which images light modulated by first light modulator 16 onto rear-projection screen 23 may comprise one or more mirrors, lenses or other optical elements. Such an optical system has the function of imaging light modulated by the first light modulator onto a second light modulator.

In the illustrated embodiment, rear-projection screen 23 comprises a second light modulator 20 and a collimator 18. A main function of collimator 18 is to cause light which passes through rear-projection screen 23 to be directed preferentially toward a viewing area. Collimator 18 may comprise a Fresnel lens, a holographic lens, or, in the alternative, another arrangement of one or more lenses and/or other optical elements which will guide light in the direction of a viewing area.

In the illustrated embodiment, collimator 18 causes light to travel through the elements of second light modulator 20 in a direction which is generally normal to screen 23. As light incident from collimator 18 travels through second light modulator 20 it is further modulated. The light then passes to a diffuser 22 which scatters the outgoing light through a range of directions so that a viewer located on an opposite side of diffuser 22 from first light modulator 16 can see light originating from the whole area of screen 23. In general, diffuser 22 may scatter light to a different angular extent in the horizontal and vertical planes. Diffuser 22 should be selected so that light modulated by second light modulator 20 is scattered through a range of angles such that the maximum scatter angle is at least equal to the angle subtended by screen 23 when viewed from a desired viewing location.

Rear-projection screen 23 may differ in area from first light modulator 16. For example, rear-projection screen 23 may be larger in area than first light modulator 16. Where this is the case, optical system 17 expands the beam of light modulated by first light modulator 16 to illuminate a larger corresponding area on rear-projection screen 23.

Second light modulator 20 may be of the same type as first light modulator 16 or a different type. Where first and second light modulators 16 and 20 are both of types that polarize light, second light modulator 20 should, as much as is practical, be oriented so that its plane of polarization matches that of the light incident on it from first light modulator 16.

Display 10 may be a color display. This may be achieved in various ways including:

-   -   making one of first light modulator 16 and second light         modulator 20 a color light modulator;     -   providing a plurality of different first light modulators 16         operating in parallel on different colors ; and,     -   providing a mechanism for rapidly introducing different color         filters into the light path ahead of second light modulator 20.

As an example of the first approach above, second light modulator 20 may comprise an LCD panel having a plurality of pixels each comprising a number of colored sub-pixels. For example, each pixel may comprise three sub-pixels, one associated with a red filter, one associated with a green filter and one associated with a blue filter. The filters may be integral with the LCD panel.

As shown in FIG. 1A, light source 12, first light modulator 16 and optical system 17 may all be parts of a digital video projector 37 located to project an image defined by a signal 38A from a controller 39 onto the back side of rear-projection screen 23. The elements of second light modulator 20 are controlled by a signal 38B from controller 39 to provide an image to a viewer which has a high dynamic range.

As shown in FIG. 2, a display 10A according to the invention may comprise one or more additional light modulation stages 24. Each additional light modulation stage 24 comprises a collimator 25, a light modulator 26 and an optical system 27 which focuses light from light modulator 26 onto either the next additional light modulation stage 24 or on collimator 18. In device 10A of FIG. 2 there are two additional light modulation stages 24. Devices according to this embodiment of the invention may have one or more additional light modulation stages 24.

The luminance of any point on output diffuser 22 can be adjusted by controlling the amount of light passed on by corresponding elements of light modulators 16, 20 and 26. This control may be provided by a suitable control system (not shown in FIG. 2) connected to drive each of light modulators 16, 20 and 26.

As noted above, light modulators 16, 20 and 26 may all be of the same type or may be of two or more different types. FIG. 3 illustrates a display 10B according to an alternative embodiment of the invention which includes a first light modulator 16A which comprises a deformable mirror device. A deformable mirror device is a “binary” device in the sense that each pixel may be either “on” or “off”. Different apparent brightness levels may be produced by turning a pixel on and off rapidly. Such devices are described, for example, in U.S. Pat. Nos. 4,441,791 and, 4,954,789 and are commonly used in digital video projectors. Light source 12 and first light modulator 16 (or 16A) may be the light source and modulator from a commercial digital video projector, for example.

FIG. 4 illustrates a front-projection-type display 10C according to the invention. Display 10C comprises a screen 34. A projector 37 projects an image 38 onto screen 34. Projector 37 comprises a suitable light source 12, a first light modulator 16 and an optical system 17 suitable for projecting an image defined by first light modulator 16 onto screen 34. Projector 37 may comprise a commercially available display projector. Screen 34 incorporates a second light modulator 36. Second light modulator 36 comprises a number of addressable elements which can be individually controlled to affect the luminance of a corresponding area of screen 34.

Light modulator 36 may have any of various constructions. For example, light modulator 36 may comprise an array of LCD elements each having a controllable transmissivity located in front of a reflective backing. Light projected by projector 37 passes through each LCD element and is reflected back through the LCD element by the reflective backing. The luminance at any point on screen 34 is determined by the intensity of light received at that point by projector 37 and the degree to which light modulator 36 (e.g. the LCD element at that point) absorbs light being transmitted through it.

Light modulator 36 could also comprise an array of elements having variable retro-reflection properties. The elements may be prismatic. Such elements are described, for example, in Whitehead, U.S. Pat. No. 5,959,777 entitled Passive High Efficiency Variable Reflectivity Image Display Device and, Whitehead et al., U.S. Pat. No. 6,215,920 entitled Electrophoretic, High Index and Phase Transition Control of Total Internal Reflection in High Efficiency Variable Reflectivity Image Displays.

Light modulator 36 could also comprise an array of electrophoretic display elements as described, for example, in Albert et al., U.S. Pat. No. 6,172,798 entitled Shutter Mode Microencapsulated Electrophoretic Display; Comiskey et al., U.S. Pat. No. 6,120,839 entitled Electro-osmotic Displays and Materials for Making the Same; Jacobson, U.S. Pat. No. 6,120,588 entitled: Electronically Addressable Microencapsulated Ink and Display; Jacobson et al., U.S. Pat. No. 6,323,989 entitled Electrophoretic Displays Using Nanoparticles; Albert, U.S. Pat. No. 6,300,932 entitled Electrophoretic Displays with Luminescent Particles and Materials for Making the Same or, Comiskey et al., U.S. Pat. No. 6,327,072 entitled Microcell Electrophoretic Displays.

As shown in FIGS. 6A and 6B, screen 34 preferably comprises a lens element 40 which functions to direct light preferentially toward the eyes of viewers. In the illustrated embodiment, lens element 40 comprises a Fresnel lens having a focal point substantially coincident with the apex of the cone of light originating from projector 37. Lens element 40 could comprise another kind of lens such as a holographic lens. Lens element 40 incorporates scattering centers 45 which provide a desired degree of diffusion in the light reflected from screen 34. In the illustrated embodiment, second light modulator 36 comprises a reflective LCD panel having a large number of pixels 42 backed by a reflective layer 43 and mounted on a backing 47.

Where light modulator 36 comprises an array of elements having variable retro-reflection properties, the elements themselves could be designed to direct retro-reflected light preferentially in a direction of a viewing area in front of screen 34. Reflective layer 43 may be patterned to scatter light to either augment the effect of scattering centers 45 or replace scattering centers 45.

As shown in FIG. 4, a controller 39 provides data defining image 38 to each of first light modulator 16 and second light modulator 36. Controller 39 could comprise, for example, a computer equipped with a suitable display adapter. Controller 39 may comprise image processing hardware to accelerate image processing steps. The luminance of any point on screen 34 is determined by the combined effect of the pixels in first light modulator 16 and second light modulator 36 which correspond to that point. There is minimum luminance at points for which corresponding pixels of the first and second light modulators are set to their “darkest” states. There is maximum luminance at points for which corresponding pixels of the first and second light modulators are set to their “brightest” states. Other points have intermediate luminance values. The maximum luminance value might be, for example, on the order of 10⁵ cd/m². The minimum luminance value might be, for example on the order of 10⁻²cd/m².

The cost of a light modulator and its associated control circuitry tends to increase with the number of addressable elements in the light modulator. In some embodiments of the invention one of the light modulators has a spatial resolution significantly higher than that of one or more other ones of the light modulators. When one or more of the light modulators are lower-resolution devices the cost of a display according to such embodiments of the invention may be reduced. In color displays comprising two or more light modulators, one of which is a color light modulator (a combination of a plurality of monochrome light modulators may constitute a color light modulator as shown, for example, in FIG. 6) and one of which is a higher-resolution light modulator, the higher-resolution light modulator should also be the color light modulator. In some embodiments the higher-resolution light modulator is imaged onto the lower-resolution light modulator. In other embodiments the lower-resolution light modulator is imaged onto the higher-resolution light modulator.

FIG. 5 illustrates one possible configuration of pixels in a display 10 as shown in FIG. 1. Nine pixels 42 of a second light modulator 20 correspond to each pixel 44 of a first light modulator 16. The number of pixels 42 of second light modulator 20 which correspond to each pixel 44 of first light modulator 16 may be varied as a matter of design choice. Pixels 44 of the higher-resolution one of first and second light modulators 16 and 20 (or 36) should be small enough to provide a desired overall resolution. In general there is a trade off between increasing resolution and increasing cost. In a typical display the higher-resolution light modulator will provide an array of pixels having at least a few hundred pixels in each direction and more typically over 1000 pixels in each direction.

The size of pixels 44 of the lower-resolution one of the first and second light modulators determines the scale over which one can reliably go from maximum intensity to minimum intensity. Consider, for example, FIG. 5A which depicts a situation where one wishes to display an image of a small maximum-luminance spot on a large minimum-luminance background. To obtain maximum luminance in a spot 49, those pixels of each of the first and second light modulators which correspond to spot 49 should be set to their maximum-luminance values. Where the pixels of one light modulator are lower in resolution than pixels of the other light modulator then some pixels of the lower-resolution light modulator will straddle the boundary of spot 49. This is the case, for example, in FIG. 5A.

Outside of spot 49 there are two regions. In region 48 it is not possible to set the luminance to its minimum value because in that region the lower-resolution light modulator is set to its highest luminance value. In region 47 both of the light modulators can be set to their lowest-luminance values. If, for example, each of the first and second light modulators has a luminance range of 1 to 100 units, then spot 49 might have a luminance of 100×100=10,000 units, region 48 would have a luminance of 100×1=100 units and region 47 would have a luminance of 1×1=1 units.

As a result of having one of the light modulators lower in resolution than the other, each pixel of the lower-resolution light modulator corresponds to more than one pixel in the higher-resolution light modulator. It is not possible for points corresponding to any one pixel of the lower-resolution light modulator and different pixels of the higher-resolution light modulator to have luminance values at extremes of the device's dynamic range. The maximum difference in luminance between such points is determined by the dynamic range provided by the higher-resolution light modulator.

It is generally not a problem that a display is not capable of causing closely-spaced points to differ in luminance from one another by the full dynamic range of the display. The human eye has enough intrinsic scatter that it is incapable of appreciating large changes in luminance which occur over very short distances in any event.

In a display according to the invention which includes both a lower-resolution spatial light modulator and a higher-resolution spatial light modulator, controller 39 may determine a value for each pixel of the lower-resolution spatial light modulator and adjust the signals which control the higher-resolution spatial light modulator to reduce artefacts which result from the fact that each pixel of the lower-resolution spatial light modulator is common to a plurality of pixels of the higher-resolution spatial light modulator. This may be done in any of a wide number of ways.

For example, consider the case where each pixel of the lower-resolution spatial light modulator corresponds to a plurality of pixels of the higher-resolution spatial light modulator. Image data specifying a desired image is supplied to the controller. The image data indicates a desired luminance for an image area corresponding to each of the pixels of the higher-resolution spatial light modulator. The controller may set the pixels of the lower-resolution light modulator to provide an approximation of the desired image. This could be accomplished, for example, by determining an average or weighted average of the desired luminance values for the image areas corresponding to each pixel of the lower-resolution light modulator.

The controller may then set the pixels of the higher-resolution light modulator to cause the resulting image to approach the desired image. This could be done, for example, by dividing the desired luminance values by the known intensity of light incident from the lower-resolution light modulator on the corresponding pixels of the higher-resolution light modulator. Processing to generate the signals for driving the light modulators may be performed on the fly by controller 39, may be performed earlier by controller 39 or some other device and integrated into the image data or some processing may be performed earlier and controller 39 may perform final processing to generate the control signals.

If the low-resolution pixels are too large then a viewer may be able to discern a halo around bright elements in an image. The low resolution pixels are preferably small enough that the appearance of bright patches on dark backgrounds or of dark spots on bright backgrounds is not unacceptably degraded. It is currently considered practical to provide in the range of about 8 to about 144, more preferably about 9 to 36, pixels on the higher-resolution light modulator for each pixel of the lower-resolution light modulator.

The sizes of steps in which each of pixels 42 and 44 can adjust the luminance of point(s) on the image are not necessarily equal. The pixels of the lower-resolution light modulator may adjust light intensity in coarser steps than the pixels of the higher-resolution light modulator. For example, the lower-resolution light modulator may permit adjustment of light intensity for each pixel over an intensity range of 1 to 512 units in 8 steps while the higher-resolution light modulator may permit adjustment of the light intensity for each pixel over a similar range in 512 steps. While pixels 42 and 44 are both illustrated as being square in FIG. 5, this is not necessary. Pixels 42 and/or 44 could be other shapes, such as rectangular, triangular, hexagonal, round, or oval.

The pixels of the lower-resolution light modulator preferably emit light which is somewhat diffuse so that the light intensity varies reasonably smoothly as one traverses pixels of the lower-resolution light modulator. This is the case where the light from each of the pixels of the lower-resolution light modulator spreads into adjacent pixels, as shown in FIG. 7. As shown in FIG. 7A, the intensity profile of a pixel in the lower-resolution light modulator can often be approximated by gaussian spread function convolved with a rectangular profile having a width d₁ equal to the active width of the pixel. The spread function preferably has a full width at half maximum in the range of 0.3×d₂ to 3×d₂, where d₂ is the center-to-center inter-pixel spacing, to yield the desired smoothly varying light intensity. Typically d₁ is nearly equal to d₂.

In the embodiment of FIG. 5, each pixel 42 comprises three sub pixels 43R, 43G and 43B (for clarity FIG. 5 omits sub pixels for some pixels 42). Sub-pixels 43R, 43G and 43B are independently addressable. They are respectively associated with red, green and blue color filters which are integrated into second light modulator 20. Various constructions of LCD panels which include a number of colored sub-pixels and are suitable for use in this invention are known in the art.

For front projection-type displays (for example the display 10C of FIG. 4), it is typically most practical for first light modulator 16 to comprise a high-resolution light modulator which provides color information and for light modulator 36 to comprise a monochrome light modulator. Light modulator 36 preferably has reasonably small addressable elements so that the boundaries of its elements do not form a visually distracting pattern. For example, light modulator 36 may have the same number of addressable elements as projector 37 (although each such element will typically have significantly larger dimensions than the corresponding element in light modulator 16 of projector 37).

Projector 37 may have any suitable construction. All that is required is that projector 37 be able to project light which has been spatially modulated to provide an image onto screen 34. FIG. 6 illustrates a display system 10D according to a further alternative embodiment of the invention. System 10D comprises a screen 34 which has an integrated light modulator 36 as described above with reference to FIG. 4. System 10D comprises a projector 37A which has separate light modulators 16R, 16G and 16R for each of three colors. Light modulated by each of light modulators 16R, 16G and 16R is filtered by a corresponding one of three colored filters 47R, 47G and 47B. The modulated light is projected onto screen 34 by optical systems 17. A single light source 12 may supply light to all three light modulators 16R, 16G, and 16B, or separate light sources (not shown) may be provided.

As will be apparent to those skilled in the art in the light of the foregoing disclosure, many alterations and modifications are possible in the practice of this invention without departing from the spirit or scope thereof. For example:

-   -   diffuser 22 and collimator 18 could be combined with one         another;     -   diffuser 22 and collimator 18 could be reversed in order;     -   multiple cooperating elements could be provided to perform light         diffusion and/or collimation;     -   the order in screen 23 of second light modulator 20 collimator         18 and diffuser 22 could be varied;     -   the signal 38A driving first light modulator 16 may comprise the         same data driving second light modulator 20 or may comprise         different data.         Accordingly, the scope of the invention is to be construed in         accordance with the substance defined by the following claims. 

1. A display controller, the controller connectible to: receive image data defining a desired image; and, control light outputs of pixels in a first array of pixels and light transmission of pixels of a second array of pixels illuminated by light emitted by the first array of pixels, the controller configured to: generate control signals for the first array of pixels to yield an approximation of the desired image on the second array of pixels; determine light intensities of the approximation at pixels of the second array of pixels; and generate control signals for the pixels of the second array of pixels based at least in part on differences between the determined light intensities and the desired image at the pixels of the second array of pixels.
 2. A controller according to claim 1 wherein, for each pixel of the first array of pixels, the second array of pixels has more than one pixel, and wherein the controller is configured to: set a pixel of the first array of pixels to contribute a luminance which is an average, or weighted average, of a plurality of desired luminance values for image areas of the first array of pixels that correspond to that pixel of the first array of pixels.
 3. A controller according to claim 1 wherein the controller is configured to: control the pixels of the second array of pixels to modulate light incident thereon based on desired luminance values at image locations corresponding to locations of the pixels of the second array of pixels divided by the determined intensities of light from the first array of pixels at the pixels of the second array of pixels.
 4. A controller according to claim 1 wherein the controller is configured to: set a pixel of the first array to pixels to a brightness level selected from a number N of discrete brightness levels; and set a pixel of the second array of pixels to a brightness level selected from a number M of discrete brightness levels, wherein N is greater than M.
 5. A controller according to claim 1 wherein the controller is configured to: set a pixel of the first array of pixels to a brightness level selected from a number N of discrete brightness levels; and set a pixel of the second array of pixels to a brightness level selected from a number M of discrete brightness levels, wherein N is less than M.
 6. A controller according to claim 1 wherein the pixels of the second array of pixels have controllable retro-reflection properties, and wherein the controller is configured to control the pixels of the second array of pixels by adjusting retro-reflection properties of the pixels of the second array of pixels.
 7. A controller according to claim 1 wherein the pixels of the second array of pixels have controllable transmission properties, and wherein the controller is configured to control the pixels of the second array of pixels by adjusting transmission properties of the pixels of the second array of pixels.
 8. A controller according to claim 1 wherein the first array of pixels comprises an array of color pixels, wherein the controller is configured to control the pixels of the first array of pixels by separately setting a color value for each pixel of the first array of pixels.
 9. A controller according to claim 8 wherein the controller is configured to control the pixels of the first array of pixels by separately setting a plurality of color values for each pixel of the first array of pixels.
 10. A controller according to claim 1 wherein the controller is configured to determine the light intensities of the approximation at pixels of the second array of pixels by estimating light emitted from the first array of pixels.
 11. A controller according to claim 10 wherein the controller is configured to estimate the light emitted from the first array of pixels based at least in part on a spread function of a pixel of the first array of pixels.
 12. A controller according to claim 11 wherein the spread function of the pixel of the first array of pixels has a full width at half-maximum in the range of 0.3×d₂ to 3×d₂, where d₂ is a center-to-center inter-pixel spacing of pixels of the first array of pixels.
 13. A controller according to claim 1 wherein the controller is configured to determine the light intensities of the approximation at pixels of the second array of pixels by, for a pixel of the second array of pixels, calculating a contribution from each of a plurality of pixels of the first array of pixels which illuminate that pixel of the second array of pixels.
 14. A controller according to claim 13 wherein the controller is configured to calculate the contribution from each of the plurality of pixels of the first array of pixels which illuminate that pixel of the second array of pixels based at least in part on a spread function of a pixel of the first array of pixels.
 15. A controller according to claim 14 wherein the spread function of the pixel of the first array of pixels has a full width at half-maximum in the range of 0.3×d₂ to 3×d₂, where d₂ is a center-to-center inter-pixel spacing of pixels of the first array of pixels.
 16. A display comprising: a first array of pixels connected to emit individually-controlled amounts of light onto a second array of pixels, the second array of pixels connected to pass individually-controllable portions of the light; and, a controller connected to: control the pixels of the first and second arrays of pixels, the controller configured to control the pixels of the first array of pixels to provide on the second array of pixels an approximation of an image specified by image data; determine a difference between the image and the approximation of the image at individual pixels of the second array of pixels; and control the pixels of the second array of pixels to modulate the approximation of the image according to the corresponding determined differences.
 17. A display according to claim 16 wherein a pixel of the first array of pixels emits light onto a plurality of pixels of the second array of pixels, and light from a plurality of pixels of the first array of pixels is incident on a pixel of the second array of pixels.
 18. A display according to claim 16 wherein the first array of pixels has fewer pixels than the second array of pixels.
 19. A display according to claim 16 wherein light emitted by a pixel of the first array of pixels is characterized by a spread function having a full width at half-maximum in the range of 0.3×d₂ to 3×d₂, where d₂ is a center-to-center inter-pixel spacing of pixels of the first array of pixels.
 20. A display according to claim 16 wherein the controller is configured to: control a pixel of the first array of pixels to emit light having a brightness level selected from a number N of discrete brightness levels; and control a pixel of the second array of pixels to have a transmissivity level selected from a number M of discrete transmissivity levels, wherein N is greater than M.
 21. A display according to claim 16 wherein the controller is configured to: control a pixel of the first array of pixels to emit light having a brightness level selected from a number N of discrete brightness levels; and control a pixel of the second array of pixels to have a transmissivity level selected from a number M of discrete transmissivity levels, wherein N is less than M.
 22. A display according to claim 16 comprising a diffuser located on a side of the second array of pixels which faces away from the first array of pixels.
 23. A display according to claim 16 comprising an optical system positioned between the first array of pixels and the second array of pixels for imaging the light emitted by the pixels of the first array of pixels onto the second array of pixels.
 24. A method of displaying an image on a display comprising a first array of pixels which emit light onto a second array of pixels, the method comprising: controlling the first array of pixels to yield a pattern of light which approximates an image specified by image date on the second array of pixels; determining a difference between the pattern of light at a pixel of the second array of pixels and a corresponding location of the image specified by the image data; and, controlling the pixel of the second array of pixels based on the determined difference.
 25. A method according to claim 24 wherein determining the difference comprises estimating an intensity of light incident on the pixel of the second array of pixels.
 26. A method according to claim 24 comprising determining an intensity of light incident on the pixel of the second array of pixels based at least in part on a spread function of the first array of pixels.
 27. A method according to claim 24 comprising: selecting a brightness level of a pixel of the first array of pixels from a number N of discrete brightness levels; and, selecting a transmissivity level of the pixel of the second array of pixels from a number M of discrete transmissivity levels, wherein N is greater than M.
 28. A method according to claim 24 comprising: selecting a brightness level of a pixel of the array of pixels from a number N of discrete brightness levels; and, selecting a transmissivity level of the pixel of the second array of pixels from a number M of discrete transmissivity levels, wherein N is less than M. 